Setting out Labour's Brexit position, he added: "We are leaving the European Union, but we will not support a deal cobbled together by a divided and chaotic Tory government if it's going to make life tougher for millions of people".
FILE - A vehicle crosses over the border from the Irish Republic into Northern Ireland near the town of Jonesborough, Northern Ireland, Jan. 30, 2017.
A senior European Union official later said Mrs May had indicated she was "ready to consider" a longer transition period.
The EU is now aiming for the December summit to get the deal done, according to one of the officials, though the idea of a November meeting hasn't been ruled out.
European Commission president Jean-Claude Juncker predicted on Thursday that a Brexit deal "will be done" despite recent setbacks.
Arriving for the talks, he said "we need time, we need much more time" for talks, vowing to work "calmly and patiently" for a deal in the coming weeks.
Asked if it would only be for a few months, he said: "Yes, that is certainly the intention".
With the impasse likely to continue, diplomats are beginning to expect that a deal might not be complete until December or January, making it very tight to ratify any agreement in domestic parliaments across the European Union, including the House of Commons.
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The Taoiseach said he and Mrs May were "in broad agreement" on the idea that the backstop could not be time-limited.
London is the focal point for clearing derivatives in the U.S. dollar and the euro, but the European authorities want all activity in euros to take place within the EU after Brexit.
Pro-EU politicians, meanwhile, said the proposal was another sign of May's weak bargaining hand and an attempt to stall for time.
May's suggestion that she'd be willing to extend the Brexit transition period by up to one year has predictably led to outrage among Conservative MPs and cries of "I told you so" from the opposition.
He added: "No Prime Minister should negotiate a deal that threatens jobs".
Both sides stress that there was progress on other unresolved issues, such as how the withdrawal agreement could be governed, and any role for the European Court of Justice, and the mutual recognition of Geographical Indications, such as Champagne, and Welsh Caerphilly.
"They are trying to leave this so late that they can credibly say there is no alternative but a "no-deal" Brexit, and most people agree that would be chaos", Boles told the BBC.
Sa vie va être adaptée au cinéma — Redoine Faïd
Aucune précision n'est donnée sur le comédien susceptible d'incarner le braqueur ou une date de sortie du film. Il avait expliqué que le film lui avait servi de modèle pour sa série d'attaques de fourgons blindés.
A backstop proposed by the EU would see Northern Ireland remain in the EU customs union and single market to avoid border and customs checks.
Before the summit, Germany's Chancellor Angela Merkel issued a stern warning that Europe must be prepared for a no-deal Brexit, while France has also stepped up its planning for the potentially catastrophic scenario.
He added that Brexit was preventing a return to power sharing in Northern Ireland.
"We have put forward a proposal as to how to deal with this".
It has compounded her problems with a large rebel faction within her own party, however, and other hardcore Brexiters who fear negotiation delays and agreeing to keep Britain tied to the bloc for longer could mean the country, which is deeply divided over Brexit, ultimately never leaves.
"Now all of them are trying to distance themselves from the time bomb they created past year", he said.
The European Union has rejected United States calls to water down new derivatives clearing rules, saying lawmakers would not be "blackmailed".
"Can the Prime Minister confirm what action the Government is taking to ensure this important sector for our economy continues to be able to access the workforce it will need?"
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